Tag Archives: mathematics

Adjusting GPAs: A Statistician’s Effort to Tackle Grade Inflation

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A recent analysis of 200 colleges and universities published in the Teachers College Record found that 43 percent of all letter grades awarded in 2008 were A’s, compared to 16 percent in 1960. And Harvard’s student paper recently reported that the median grade awarded to undergraduates at the elite school is now an A-.

Via Adjusting GPAs: A Statistician’s Effort to Tackle Grade Inflation

“That allowed me to look directly at the influence of course grades on student evaluations,” Johnson said. “As you might expect, the effect of either expected course grade or received course grade is very powerful in student evaluations of teaching. If a student was getting a C in a course, he or she was very unlikely to rate the instructor highly. If they were getting an A in the course, they’re more likely to rate the instructor highly. I think this provides quantitative evidence for something most instructors know: If they grade easier, they will tend to get better course evaluations.”

How Not To Sort By Average Rating

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PROBLEM: You are a web programmer. You have users. Your users rate stuff on your site. You want to put the highest-rated stuff at the top and lowest-rated at the bottom. You need some sort of “score” to sort by.

via How Not To Sort By Average Rating.

CORRECT SOLUTION: Score = Lower bound of Wilson score confidence interval for a Bernoulli parameter

Say what: We need to balance the proportion of positive ratings with the uncertainty of a small number of observations. Fortunately, the math for this was worked out in 1927 by Edwin B. Wilson. What we want to ask is: Given the ratings I have, there is a 95% chance that the “real” fraction of positive ratings is at least what? Wilson gives the answer. Considering only positive and negative ratings (i.e. not a 5-star scale), the lower bound on the proportion of positive ratings is given by:

The Mathematics of Gamification

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At Foursquare, we have a simple, first-principles based method of resolving proposed venue attribute updates. We can gauge each Superuser’s voting accuracy based on their performance on honeypots (proposed updates with known answers which are deliberately inserted into the updates queue). Measuring performance and using these probabilities correctly is the key to how we assign points to a Superuser’s vote.

The Math

Let’s make this more concrete with some math.

via The Mathematics of Gamification | Foursquare Engineering Blog.

Academics should not remain silent on hacking

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NIST’s standard for random numbers used for cryptography, published in 2006, had been weakened by the NSA. Companies such as banks and financial institutions that rely on encryption to guarantee customer privacy depend on this standard. The nature of the subversions sounds abstruse: the random-number generator, the ‘Dual EC DRBG’ standard, had been hacked by the NSA so that its output would not be as random as it should have been. That might not sound like much, but if you are trying to break an encrypted message, the knowledge that it is hundreds or thousands of times weaker than advertised is a great encouragement.

via Academics should not remain silent on hacking : Nature News & Comment.

How Does the Tesla Model S Fire Risk Compare to Gasoline Cars?

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Since the Model S went into production last year, there have been more than a quarter million gasoline car fires in the United States alone, resulting in over 400 deaths and approximately 1,200 serious injuries (extrapolating 2012 NFPA data). However, the three Model S fires, which only occurred after very high-speed collisions and caused no serious injuries or deaths, received more national headlines than all 250,000+ gasoline fires combined. The media coverage of Model S fires vs. gasoline car fires is disproportionate by several orders of magnitude, despite the latter actually being far more deadly.

Reading the headlines, it is therefore easy to assume that the Tesla Model S and perhaps electric cars in general have a greater propensity to catch fire than gasoline cars when nothing could be further from the truth.

via The Mission of Tesla | Blog | Tesla Motors.

Scientific Data Has Become So Complex, We Have to Invent New Math to Deal With It

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Scientists like DeDeo and Vespignani make good use of this piecemeal approach to big data analysis, but Yale University mathematician Ronald Coifman says that what is really needed is the big data equivalent of a Newtonian revolution, on par with the 17th century invention of calculus, which he believes is already underway. It is not sufficient, he argues, to simply collect and store massive amounts of data; they must be intelligently curated, and that requires a global framework.

via Scientific Data Has Become So Complex, We Have to Invent New Math to Deal With It – Wired Science.

Among the most notable insights Euler gleaned from the puzzle was that the exact positions of the bridges were irrelevant to the solution; all that mattered was the number of bridges and how they were connected. Mathematicians now recognize in this the seeds of the modern field of topology.

Google wants a patent on splitting the restaurant bill

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Google Patent Application, October 2013: “For example, continuing with the example of FIG. 4, assume that Users A-C have drinks at a bar and User B pays a bill of $45 for the drinks. User B adds the payment transaction as an expenditure of the group and allocates $15 of the transaction to User A, $20 to User B, $10 to User C. In this example, the balance module 308 would update the individual balances of Users A-C to indicate that User B now owes $115 to User A ($130-$15) and User C owes $10 to User B ($0+$10).”

via No joke: Google wants a patent on splitting the restaurant bill – GeekWire.

I didn’t think one could patent a mathematical formula.

Gear up for the school year with these open source applications

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Here are five great open source applications for learning. Share this list to your favorite student or teacher!

via Gear up for the school year with these open source applications | opensource.com.

Play with math, programming, music, and art in the powerful Kojo Learning environment. Based on ideas derived from innovative programs such as Logo and Geometers Sketchpad, Kojo offers a rich platform for students to explore the synthesis of mathematical ideas, coding, creative thinking, and learning.

Weak Keys in Network Devices – Mind your RNG!

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An RSA public key (e,N) consists of an exponent e and a modulus N. The modulus is the product of two randomly chosen prime numbers p and, q. If p and q are known, it is straightforward to derive the private key. However, if they are unknown, one must factor N into p and q, which requires intensive computing resources. However, let’s assume that two keys with modulus N1 and N2 share one of the factors: N1 = p1 x q and N2 = p2 x q. In this case, finding the greatest common divisor of N1 and N2, which is q, is sufficient to factor these two moduli. The task of finding the greatest common divisor of two 1024-bit integers is much simpler than factoring and can be done in microseconds…

This well known vulnerability of RSA can be exploited in the context of low entropy keys. Poor random number generation can indeed lead to multiple keys sharing one of their factors. Heninger found that more than 60’000 keys (approximately 0.5%) they had collected could be factored in this way.

via Quantis Newsletter – September 2012.

Using Metadata to find Paul Revere

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Rest assured that we only collected metadata on these people, and no actual conversations were recorded or meetings transcribed. All I know is whether someone was a member of an organization or not. Surely this is but a small encroachment on the freedom of the Crown’s subjects. I have been asked, on the basis of this poor information, to present some names for our field agents in the Colonies to work with. It seems an unlikely task.

If you want to follow along yourself, there is a secret repository containing the data and the appropriate commands for your portable analytical engine.

via Using Metadata to find Paul Revere – Kieran Healy.